Help me with math in this NL spot.

[Ralph Wiggum]

There's $35 in the pot.

If I push and my opponent calls, there'll be $185 in the pot. I'll have a 25% chance of winning.

How do I figure how often my opponent has to fold, for my push to break even or be profitable?

[DWarrior]

I'm guessing you have $75 effective stacks.

x(35)+(1-x)(185*.25-75*.75) >= 0

x is the % of time villain folds. x must be greater than or equal to the solution for push to be breakeven/profitable.

In this case x >= 40%

[pzhon]

[ QUOTE ]
There's $35 in the pot. If I push and my opponent calls, there'll be $185 in the pot. I'll have a 25% chance of winning.

How do I figure how often my opponent has to fold, for my push to break even or be profitable?

[/ QUOTE ]
There isn't enough information. You can say how likely your opponent needs to fold to make pushing better than open-folding, but that's not your choice.

Relative to open-folding, if you push and are called, it costs you the $75 you put in by pushing minus .25 * $185 returned on average = 75-46.25 = $28.75.

Relative to open-folding, if you push and are not called, you gain the $35 pot.

Expressed in odds, you need the odds against a fold (reward) to be less than 35:28.75 (reward:risk) against in order for pushing to be better than open-folding. In probability, you need the probability of a fold (reward) to be better than 28.75/(28.75+35) (risk/(risk+reward)) for pushing to be better than open-folding.

It's much more sensible to compare pushing with checking, and to estimate that you will get something like $5 back from the pot by checking. Use your best estimate instead of $5. In that case, perform the above calculations with a reward which is decreased by $5 to $30, and a risk which is increased by $5 to $33.75.

[Ralph Wiggum]

Thanks guys.

Sorry about not giving enough info. It's was actually $9 for me to call (creating a $44 pot). Opponent had $70.xx left, and I covered. But the 40% is good enough for me.

I'll have to read your reply a couple more time pzhon to appreciate what you're saying. Math hates me.

[DWarrior]

I think what he's saying is that you have to calculate the EV of other plays as well. (Hopefully I interpret this correctly)

So you're break even if he folds 40% of the time.

However, it might be better to just check and call, or even check/fold. For example, say villain bets all better hands and checks down all worse hands, but folds all worse hands and calls all better hands, now betting is a bad play.

Say check/calling or check/folding will net you $5, now pushing has to make you more than $5 to be a better play.